Is there such thing as being able to convert a Langstroth, Dadant and British National Hive. If not, why not? What problems would arise?
If your target market is the beekeeper that uses fairly modern equipment but needs to move from the one format to the other regularly, then you can concentrate on only frame sizes.
However, if you want to help beekeepers who have been using a variety of hive sizes for many years, you may find that some of them use non-standard widths (i.e. they might use a 7-frame, 8-frame or 9-frame hive when the shop-bought standard is 10-frame or 11-frame). The other dimensions of their hives will be standard, but the hive widths will be customised. So you must decide if you want to include those people in your target market, because if you do, then you to design your system to cope also with variable hive widths. And you also get 3-frame, 4-frame and 5-frame variants, etc.
But let's suppose you are targeting beekeepers who bought their hives in a beekeeping store that sells "standard" hives, or who make their hives to the exact specifications of "official" hive plans.
Then the next thing to understand is that the names "Dadant" and "Langstroth" are fairly generic, and a store in e.g. California that sells "Langstroth" hives may sell hives that are a different size than a store in Washington that sells "Langstroth" hives. And don't forget that different countries also all have their own "Langstroth" hives of various sizes.
But, if you want to make it easy on yourself, find out which stores or manufacturers are the biggest sellers in e.g. the UK or US, and download their catalogues from their web sites, and check out what their frame and box sizes are.
By and large, a thing called a Dadant and a thing called a Langstroth used in the UK have the same frame length, but different frame heights.
By now you can understand why manufacturers who try to enter the beekeeping market with "plastic" systems prefer to simply force their customers to use their particular sizes by providing plastic frames that fit into their plastic hives. The assumption of these manufacturers is that a commercial beekeeper will adopt their system and then throw out all their old equipment and get all the new equipment. Hmmm....
Good luck with your project... you've stuck out on these forums longer than most design students.
Added: Oh, and note that the National frames have longer lugs... and if you're going to design something that will increase a box's height, have a look at the concept of top bee-space and bottom bee-space, because different hives use different one, and that becomes important when you put one type of box on top of another.